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Integration through transients for inelastic hard sphere fluids

W. Till Kranz1,2,*, Fabian Frahsa3, Annette Zippelius4, Matthias Fuchs3, and Matthias Sperl2,1

  • 1Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany
  • 2Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
  • 3Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
  • 4Institut für Theoretische Physik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany

  • *kranz@thp.uni-koeln.de
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Phys. Rev. Fluids 5, 024305 – Published 28 February, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.024305

Abstract

We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalize the Integration Through Transients formalism to a fluid of dissipative, randomly driven granular particles. The stress relaxation function is computed approximately within a mode-coupling theory—based on the physical picture that relaxation of shear is dominated by slow structural relaxation, as the glass transition is approached. The transient build-up of stress in steady shear is thus traced back to transient density correlations which are computed self-consistently within mode-coupling theory. The glass transition is signaled by the appearance of a yield stress and a divergence of the Newtonian viscosity, characterizing linear response. For shear rates comparable to the structural relaxation time, the stress becomes independent of shear rate and we observe shear thinning, while for the largest shear rates Bagnold scaling, i.e., a quadratic increase of shear stress with shear rate, is recovered. The rheological properties are qualitatively similar for all values of ɛ, the coefficient of restitution; however, the magnitude of the stress as well as the range of shear thinning and thickening show significant dependence on the inelasticity.

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Phys. Rev. Fluids 5, 024305– Published 28 February, 2020
  • Received 12 October 2017
  • Accepted 4 February 2020
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